Basic Data Analysis for Quantitative Research

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Basic Data Analysis for Quantitative Research
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Statistical Analysis

• Every set of data collected needs some summary
  information developed that describes the numbers
  it contains
• Central tendency and dispersion,
• Relationships of the sample data, and
• Hypothesis testing

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Measures of Central Tendency
Mean Arithmetic Average
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Measures of Central Tendency

• Each measure of central tendency describes a
  distribution in its own manner
• for nominal data, the mode is the best measure.
• for ordinal data, the median is generally the
  best.
• for interval or ratio data, the mean is generally
  used.

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Measures of Dispersion

• Describes how close to the mean or other measure
• of central tendency, the rest of the values fall

Range Distance between the smallest and largest
value in a set
Standard Deviation Measure of the average
dispersion of the values about the mean
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Results for Measures of Dispersion
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Hypothesis Testing

• Independent Samples
• two or more groups of responses that are tested
  as though they may come from different populations

• Related Samples
• two or more groups of responses that originated
  from the sample population

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Univariate Tests of Significance

• Tests of one variable (univariate) at a time
• Appropriate for interval or ratio data

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Bivariate Statistical Tests

• Compare characteristics of two groups or two
  variables
• Cross-tabulation with Chi-Square
• t-test to compare two means
• Analysis of variance (ANOVA) to compare three or
  more means

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Results for Cross-Tabulation
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Chi-Square Analysis
Chi-square analysis tests for statistical
significance between the frequency
distributions of two or more nominally scaled
variables in a cross-tabulation Table. The
purpose of the analysis is to determine if there
is any association (relationship) between the
variables
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SPSS Chi-Square Crosstab Example
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Comparing means

• Requires interval or ratio data
• The t-value is a ratio of the difference between
  the two sample means and the std error
• The t-test tries to determine if the difference
  between the two sample means occurred by chance

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Comparing Two Means with Independent Samples
t-Test
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Paired Samples t-Test
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Analysis of Variance

• Analysis of Variance (ANOVA) is a statistical
  technique that determines if three or more means
  are statistically different from each other
• The dependent variable must be either interval or
  ratio scaled data
• The independent variable must be categorical
  (nominal scaled data)
• One-way ANOVA means that there is only one
  independent variable

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F-Test
The F-test is the test used to statistically
evaluate the differences between the group means
in ANOVA
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Determining Statistical Significance using F-Test
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Follow-up Tests

• Anova does not tell us where the significant
  differences lie just that a difference exists
• Tukey
• Duncan
• Scheffe

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ANOVA
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Perceptual Mapping
Perceptual mapping is a process that is used
develop maps showing the perceptions of
respondents. The maps visually
represent respondent perceptions in two dimensions
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Perceptual Map of Fast-Food Restaurants